Fractional order differential equations for chronic liver cirrhosis with frequent hospitalization

Area of Science:

• Mathematical modeling
• Hepatology
• Non-communicable diseases

Background:

• Liver cirrhosis is a life-threatening, terminal stage of liver disease, often linked to viral hepatitis (B and C).
• Cirrhosis progresses from asymptomatic compensated to symptomatic decompensated stages, marked by multi-systemic complications and hospitalization.
• Understanding the dynamics of chronic liver cirrhosis is crucial for managing this global non-communicable disease.

Purpose of the Study:

• To formulate a system of fractional differential equations for chronic liver cirrhosis, incorporating frequent hospitalizations.
• To investigate the disease dynamics and analyze fundamental properties like solution existence and biological feasibility.
• To develop and apply a numerical scheme for simulating the fractional order model.

Main Methods:

• Formulation of a fractional differential equation system to model chronic liver cirrhosis.
• Application of the generalized mean value theorem to establish the existence of positive solutions.
• Implementation of an Adams-type predictor-evaluate-corrector-evaluate approach for numerical simulations using MATLAB.

Main Results:

• Numerical simulations successfully illustrated the analytic findings of the fractional order model.
• The analysis indicated a reduction in decompensated cirrhosis cases when progression rate and past disease states are considered.
• The study confirmed the existence of positive solutions and the biological feasibility of the model.

Conclusions:

• Fractional differential equations provide a valuable framework for modeling complex diseases like chronic liver cirrhosis.
• The findings suggest that incorporating disease progression rates and historical data into models can inform strategies to reduce decompensated cases.
• The developed numerical scheme is effective for simulating and analyzing fractional order models in disease dynamics.